## Abstract Let __u__ and __v__ be, respectively, the solutions to the Cauchy problems for the dissipative wave equation $$u\_{tt}+u\_tβ\Delta u=0$$\nopagenumbers\end and the heat equation $$v\_tβ\Delta v=0$$\nopagenumbers\end We show that, as $t\rightarrow+\infty$\nopagenumbers\end, the norms
Weighted Decay Estimates for the Wave Equation
β Scribed by Piero D'Ancona; Vladimir Georgiev; Hideo Kubo
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 368 KB
- Volume
- 177
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We study the asymptotic behavior of solutions of dissipative wave equations with space-time-dependent potential. When the potential is only time-dependent, Fourier analysis is a useful tool to derive sharp decay estimates for solutions. When the potential is only space-dependent, a powerful techniqu
## Abstract We study the electromagnetic wave equation and the perturbed massless Dirac equation on β~__t__~ Γ β^3^: where the potentials __A__(__x__), __B__(__x__), and __V__(__x__) are assumed to be small but may be rough. For both equations, we prove the expected time decay rate of the solution
## Abstract In this paper, we study decay properties of solutions to the wave equation of pβLaplacian type with a weak dissipation of mβLaplacian type. Copyright Β© 2006 John Wiley & Sons, Ltd.